Dirac Definition and 900 Threads

Paul Adrien Maurice Dirac (; 8 August 1902 – 20 October 1984) was an English theoretical physicist who is regarded as one of the most significant physicists of the 20th century.Dirac made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics. Among other discoveries, he formulated the Dirac equation which describes the behaviour of fermions and predicted the existence of antimatter. Dirac shared the 1933 Nobel Prize in Physics with Erwin Schrödinger "for the discovery of new productive forms of atomic theory". He also made significant contributions to the reconciliation of general relativity with quantum mechanics.
Dirac was regarded by his friends and colleagues as unusual in character. In a 1926 letter to Paul Ehrenfest, Albert Einstein wrote of Dirac, "I have trouble with Dirac. This balancing on the dizzying path between genius and madness is awful." In another letter he wrote, "I don't understand Dirac at all (Compton effect)."He was the Lucasian Professor of Mathematics at the University of Cambridge, was a member of the Center for Theoretical Studies, University of Miami, and spent the last decade of his life at Florida State University.

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  1. M

    Laplace transform - Dirac delta

    i need help trying to find the laplace transform of te-t\delta(t) i know the laplace transform of te-t is 1/(s+1)2 but i don't know how to find the laplace transform of a product with the Dirac delta
  2. A

    Can Particles Described by Dirac and Klein-Gordon Equations Exist Independently?

    The component solutions of the Dirac equation are also solutions of the Klein-Gordon equation. But these solutions are not scalars since the coefficients contain quantities like energy and momentum[the phase part is of course an invariant] These are neither zero spin nor half spin...
  3. J

    Three dimensional dirac function

    Homework Statement Show that if r = \sqrt{x^2 + y^2 + z^2} then \nabla^2 \left( \frac{1}{r} \right) = -4 \pi \delta^3(r) Homework Equations I've heard Green's theorem should help me... not quite certain how. The Attempt at a Solution I took the divergence of the left hand side...
  4. S

    Is the Dirac Delta Function Even?

    Hi this is my first post here so I'm sorry if my question seems trivial. I haven't worked a lot with the dirac delta function before, so i always thought that the shifting property would only work as: \int\delta(x-h)\;f(x)\;dx=f(h) Now I've been reading some articles and I came across...
  5. E

    Dirac spinors and commutation

    Hey guys, i'm stuck (yet again! :) ) I am somewhat confused by Dirac spinors u,\bar{u}. Take the product (where Einstein summation convention is assumed): u^r u^s\bar{u}^s Is this the same as u^s\bar{u}^s u^r? Probably not because u^r is a vector while the other thing is a matrix...
  6. F

    Information content of Dirac delta function

    I understand that the Dirac delta function can be taken as a distribution. And that one can calculate the Shannon entropy or information content of any distribution. So what is the information content of the Dirac delta function? I think it is probably identically zero, but I'd like to see the...
  7. T

    Signals & Comms: Unit step function - dirac

    Homework Statement The Dirac function (unit impulse) is defined as \delta(t) = 0 where t \neq 0 the integration of d(t) between -ve inf and +ve inf is 1. Now I picture this as a rectangle with no width and infinite height. In fact I think of the width (along the x axis) as (1/inf =...
  8. P

    Exploring Dirac Matrices and Their Dimensions

    I am currently reading Dirac Equation from Peskin-Schroeder. In a particular para it says, "Now let us find Dirac Matrices \gamma^\mu for four-dimensional Minkowski Space. It turns out that these matrices must be at least 4X4." What is the proof of the above statement? I think (not sure)...
  9. J

    External Fields and Negative Energy Transitions In Dirac Particle

    Homework Statement Suppose a relativistic particle with spin 1/2 at rest. Show that if we apply an electrical field at t=0 there's a probability fot t>0 of finding the particle in a negative energy state if such negative energy states are assumed to be originally empty. Homework Equations...
  10. K

    Can quantum field theory explain the g-factor in the Dirac equation?

    To quote Weinberg Vol1, Pg 14 : And immediately he said: So to speak, Dirac equation alone cannot determine g-factor uniquely, but quantum field theory can? How?
  11. C

    Python Dirac Algorithm in Python (or similar)

    I was wondering if anybody knows of any code available to perform tensor analysis in Python or in other language; I was wondering if there is any computational method for finding constraints in a lagrangian via the Dirac Algorithm.
  12. E

    Prove that dirac matrices have a vanishing trace

    Not a Homework problem, but I think it belongs here. Homework Statement Consider four dirac matrices that obey M_i M_j + M_j M_i = 2 \delta_{ij} I knowing the property that Tr ABC = Tr CAB = Tr BCA show that the matrices are traceless. Homework Equations Tr MN = Tr NM The Attempt...
  13. J

    I've gotten stuck with a bit of dirac notation calculation?

    sorry if this looks ugly but I couldn't find out how to write out bras and kets on the Latex thing. I have these inner products <f|g> = i<x|(AB - A<B> - <A>B + <A><B>)|x> and <g|f> = -i<x|(BA - B<A> - <B>A + <A><B>)|x> where |x> is some arbitrary ket and A and B do not commute. I'm trying to...
  14. T

    Massless Dirac equation and graphene

    I am reading about the electron flow in graphene and the article said this "This behavior is not described by the traditional mathematics (Schrodinger equation) but by the mass-less Dirac equation" What does this mean and what is the massless Dirac equation... the whole paragraph is...
  15. Q

    QFT: Radiative Transitions and the Dirac Sea

    I'm completely lost on this question in our QFT course, as is everyone I have asked in the class. The professor is a crazy old man who can do this stuff in his sleep, which must be helpful for him since that's about all he does. I really have no idea what this question is asking, any guidance...
  16. arivero

    So what's the deal with Majorana, Weyl, and Dirac particles in N dimensions?

    Amusingly, a search on these three words here in PF does not show a lot of postings, so I am creating this thread so you can ask all your doubts about N-dimensional Majorana, Weyl and Dirac particles, their representations, their Lagragians, masses, and whatever you have always wanted to know...
  17. S

    Two proofs in Dirac Delta Function

    Homework Statement a.) Given \delta_n=\frac{ne^{-{n^2}{x^2}}}{\pi} Show: x{\frac{d}{dt}\delta_n}=-\delta_n b.) For the finite interval (\pi,-\pi) expand the dirac delta function \delta(x-t) in sines and cosines, sinnx, cosnx, n=1,2,3... They are not orthogonal, they are normalized to...
  18. T

    Yukawa [3 Dirac - 8 scalar] interaction lagrangian

    Homework Statement Given an interaction lagrangian L = i \, g \, \bar \psi(x)_i (\lambda^a)_{ij} \gamma_5 \, \psi(x)_j \phi(x)_a where \psi_i are three Dirac fermions with mass M and \phi_a are eight real scalar fields of mass m and \lambda_a are the generators of SU(3). I have to find...
  19. L

    Help Understanding Dirac Equation in Notes

    I have a very simple question about the Dirac equation that I just cannot see the answer to. In these notes: http://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf In equation 4.115, I keep getting u( \vec{p} ) = \begin{pmatrix} \sqrt{p \cdot \sigma} \begin{pmatrix} 1 \\ 0 \end{pmatrix} \\ \sqrt{...
  20. H

    Exploring the Relationship between Pauli and Dirac Matrices and Quaternions

    Does anybody know a good thread, homepage or book that takes up different interpretations of Pauli and Dirac matrices with the connection to for example quaternions or bivectors? Maybe someone could comment on this?
  21. L

    Decomposing the Dirac Lagrangian into Weyl Spinors

    If we take the the Dirac Lagrangian and decompose into Weyl spinors we find \mathcal{L} = \bar{\psi} ( i \gamma^\mu \partial_\mu - m ) \psi = i U^\dagger_- \sigma^\mu \partial_\mu u_- + i u^\dagger_+ \bar{\sigma}^\mu \partial_\mu u_+ - m(u^\dagger_+ u_- + u^\dagger_- u_+ ) =0 So far I have...
  22. H

    Line charge density expressed via Dirac delta function

    Homework Statement Let's say we have a wire of finite length L with total charge Q evenly spread along the wire so that lambda=Q/L, linear charge density, is constant. The wire is shaped in x-y plane in some well behaved curve y = f(x). Find the surface charge density sigma(x,y). Homework...
  23. B

    Lorentz transform on the Dirac equation

    Homework Statement Show that a Lorentz transformation preserves the sign of the energy of a solution to the Dirac equation. The Attempt at a Solution I'm not sure how to approach this. So I apply the Lorentz transform to the Dirac equation, and work through it to obtain the energy...
  24. G

    Why Might Dirac Bilinears Not Zero Out for Non-Diagonal Components?

    Hi, I have free solutions of Dirac equation in the form (without exp(), i also use the contracted 2 dimensional convection ): for r=1,2 E=E_p \omega^{r=1,2}(\vec{p}) = N \[ \left( \begin{array}{c} \phi_r \\ \phi_r c \frac{\vec{\sigma}\cdot\vec{p}}{E_p + mc^2} \end{array} \right)\]...
  25. B

    Understanding Dirac Notation: Tips for Completing Confusing Homework Problems

    Homework Statement Please see attached Homework Equations The Attempt at a Solution Ok so basically a bit confused about notation.. does |psi> = sum over all r of ar |ur> ? any help would be great..thanks
  26. P

    Dirac algebra of constraints in GR

    In hamiltonian formulation of GR there appears some constraints (it may be found e.g. in "Modern canonical quantum GR" by Theimann, ch. 1.2). I would like to find a Dirac algebra of the constraints (i.e. compute Poisson bracket between constraints), but my results are not consistent with...
  27. G

    Solving the Dirac Equation for the Hydrogen Atom

    Would someone tell me some website where I can find the relativistic treatment of the hydrogen atom using Dirac's Equation? I am not trying the find the method which uses Schrodinger's equation and adds as perturbations fine and hyperfine structures? Thank you. So far i have not find anything...
  28. H

    Can I Calculate Traces and Cross Sections in QED Using Gamma Matrices?

    hi how to calculate the traces of product of Dirac matrices in QED. i want caculate crossection of process scattering in QED. a program to calculate it
  29. Y

    How to Construct Gamma Matrices in Higher Dimensions Using Sigma Matrices?

    Homework Statement If D =7 and the metric g\mu\nu=diag(+------), Using the outer product of matrices, A \otimes B construct a suitable set of \gamma matrices from the 2 x 2 \sigma-matrices Homework Equations \sigma1=(0, 1 ) \sigma2=(0, -i)...
  30. H

    Help Understanding Dirac Delta Function in Lecture Notes

    I don't understand in the first paragraph of the attached lecture notes. Could anyone help?
  31. P

    Confusion about How Dirac discovered Dirac's Equation

    When I learned about Dirac's Equation, textbooks usually say that the earlier Klein-Gordon equation isn't linear in time derivative, contrary to what we expect from the time-dependent Schrodinger equation, therefore Dirac had to come up with a version that's linear. However, I think this doesn't...
  32. N

    QM: Understanding the Dirac notation

    Homework Statement Hi guys Ok, I have some questions, which I would very much like for you guys to help me with. Say I have some state |1>, which denotes the first, n=1, solution of the infinite, square well. |1> is a vector in the Hilbert space spanned by all the eigenvectors of the...
  33. R

    Dirac brackets and gauge in special relativity.

    Hello, It's well known that the action for a relativistic point particle is: S=-m\int d\tau\left(-\dot{x}^2\right)^{1/2} the canonical momentum is p_{\mu}= \frac{m\dot{x}_{\mu}}{\left(-\dot{x}^2\right)^{1/2}}. This action is invariant under reparametrizations of \tau, then its...
  34. B

    Simplifying Quantum Mechanics with Dirac Notation

    Homework Statement trying to simplify (using dirac notation) QM: <E| (QH - HQ) |E> using H|E> = E|E> Homework Equations The Attempt at a Solution the textbook says that it simplifies to (E-E) <E|Q|E> = 0 but i can't see how :S
  35. R

    Calculating <\chi_3|H|\chi_3> w/ Dirac Notation Algebra

    Say we have, |\chi_3>=|a+ib> and we want : <\chi_3|H|\chi_3> is it correct to say: <\chi_3|H|\chi_3>= <a|H|a>+<a|H|ib>+<-ib|H|a>+<-ib|H|ib> ??
  36. R

    Dirac Delta as Gaussian functions

    I am looking at a problem, part of which deals with expressing delta dirac as a limiting case of gaussian function. I am aware of the standard ways of doing it. In addition, I would also like to know if the following are correct - \delta(x-a) = \lim_{\sigma \rightarrow{0}} \int_{a -...
  37. maverick280857

    Dirac Spinor Algebra: Simplifying Expressions

    Hi, In a calculation I am doing, I encounter terms of the form \bar{u}^{s_1}(\boldsymbol{\vec{p}})\gamma^{\mu}{v}^{s_2}(\boldsymbol{\vec{q}}) where u and v are the electron and positron spinors. Is there any recipe for simplifying this expression, using the spin sums or other identities? I am...
  38. F

    Multivariable Dirac Delta Functions

    Hello all. So I am trying to integrate a function of this form: \int\intF(x,y)\delta[a(Cos[x]-1)+b(Cos[y]+1)]dxdy The limits of integration for x and y are both [0,2Pi). I know that this integral is only nonzero for x=0, y=Pi. So this should really only sample one point of F(x,y)...
  39. L

    Fourier Transform and Dirac Delta Function

    Homework Statement I am new to FT and dirac delta function. Given the following signal: x\left(t\right)=cos\left(2\pi5t\right)+cos\left(2\pi10t\right)+cos\left(2\pi20t\right)+cos\left(2\pi50t\right) I use the online calculator to find me the FT of the signal, which is...
  40. maverick280857

    Quantized Dirac Field Interacting with a Classical Potential

    Hi, I'm working through Section 4-3 of Itzykzon and Zuber's QFT textbook, but I am a bit stuck while trying to understand some of the quantities and equations. First of all, what is this "one-body scattering operator \mathcal{F}(A)"? It is defined (eqn 4-89, page 188) as \mathcal{F}(A) =...
  41. C

    Derivation of Dirac Delta Function

    Hello, My question is about how dirac-delta function is derived by using this integral, \frac{1}{2\pi }\int_{-\infty}^{\infty}e^{ikx}dk=\delta (x) I couldn't solve this integral. Please help me. Thanks for all of your helps.
  42. C

    Fermi dirac distribution at T->0

    Studying the free electron model I found the fermi dirac distribution and the book told me that when T->0 we have that the fermi energy is equal to the chemical potential... why?
  43. J

    I need the dirac notation expectation value explaining to me please?

    Hi, I find a lot of the time in QM i have been calculating things blindly. Take the expectation value for instance. I have worked this out in integral form plenty of times, but haven't really understood why I'm doing what I'm doing. I looked up wikipedia and apparently, for a measurable...
  44. H

    Dirac delta integrated from 0 to infinity

    I was wondering if I integrate the dirac delta function from 0 to infinity where the function it's integrated with is the constant 1, will I get 0.5 or 1? And why? This is not homework so I decided to post this here although I asked this question in class and the teacher (assistant) wasn't...
  45. M

    Plotting Dirac Delta Function in Maple14: Troubleshooting

    Homework Statement I want to plot the following function into Maple14. \vec{v}=frac{1}{\vec{r^{2}}} \hat{r} **In case the latex is screwed this says v=r^(-2) *r-hat The Attempt at a Solution My code for Maple is the following, but it doesn't seem to work.restart; with(LinearAlgebra)...
  46. W

    Proofs for Dirac delta function/distribution

    [SOLVED] Proofs for Dirac delta function/distribution Homework Statement Prove that \delta(cx)=\frac{1}{|c|}\delta(x) Homework Equations \delta(x) is defined as \delta(x)=\left\{\stackrel{0 for x \neq 0}{\infty for x=0} It has the properties...
  47. V

    Integral of dirac delta function at x=0

    Hi Can somebody help me with this... Is is correct to say that, Integral(delta(0)) = 1 (limits are from -infinity to +infinity) I don't know latex and sorry for the inconvenience in readability. Thanks, VS
  48. L

    Please help with Quantum Mechanics Dirac Delta Problems

    These problems are from Introductory Quantum Mechanics (Liboff, 4th Ed.) Note: I'm using "D" as the dirac delta function. 3.9 (a) Show that D( sqrt(x) ) = 0 This has me stumped. It is my understanding that the Dirac function is 0, everywhere, except at x=0. So, how can I show this to be...
  49. W

    Dirac equation in one dimension

    i am now studying dirac equation and klein paradox if we confine to one dimension, we only need one alpha matrix, not three so in lower dimensions, maybe the dirac spinor is not of four components but fewer? i am curious about this question because it seems that as for the Klein...
  50. A

    Power expansion of the Dirac Delta function?

    Hi, I hope this is the right place to ask this Is it possible to expand the Dirac delta function in a power series? \delta(x)=\sum a_n x^n If so, what's the radius of convergence or how can I find it? Thanks.
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